I find it necessary to add 1/3 or 2/3 additional exposure in both AV and M (flash) mode with my new 5D3.

Av mode your flash will work as a fill-in flash, in M mode the flash will provide enough light based upon the ISO, shutter speed, and aperture selected. ISO 400 is a good starting point for M use with flash and possibly 800 since the ISO is so good.